John Wormell is an undergraduate student majoring in Mathematics and Linguistics at the University of Sydney. He is interested in dynamical systems and computational mathematics, especially as they apply to statistics. More specifically, his work examines methods to efficiently characterise and evaluate components of complicated systems, primarily using traditional analytic techniques. Current projects include investigating periodic solutions to non-linear inhomogeneous PDEs associated with light propagation in fibre optic cables and developing methods to accurately calculate exact tests using Fast Fourier Transforms.
A fast and numerically robust method for computing Pearson’s exact multinomial goodness-of-fit test
Exact tests are tests for which the statistical significance is computed from the underlying distribution rather than, say using Monte Carlo simulations or saddle point approximations. Despite of their accuracy exact tests are often passed over as they tend to be too slow to be used in practice. We recently developed a technique that fuses ideas from large-deviation theory with the FFT (Fast Fourier Transform) that can significantly speed up the evaluation of some exact tests. In this project we would like to explore the applicability of our approach to a wide set of tests.